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# Physics Help Please?

1) A 1.79 kg mass attached to a light string rotates on a horizontal frictionless table. The radius of the circle is 0.912 m, and the string can support a mass of 27.7 kg before breaking.

The acceleration of gravity is 9.8 m/s/s.

What maximum speed can the mass have before the string breaks? (answer in units of m/s)

2) A sample of blood is placed in a centrifuge of radius 11.6 cm. The mass of a red blood is 4.1 x 10^ -16 kg, and the magnitude of the force acting on it as it settles out of the plasma is 4.4 x 10^ -11 N.

At how many revolutions per second should the centrifuge be operated? Answer in units of rev/s.

Thanks!

### 1 Answer

- Anonymous1 decade agoFavorite Answer
1.

If v is the maximum speed:

1.79 * v^2 / 0.912 < 27.7 * 9.81

v < sqrt(0.912 * 27.7 * 9.81 / 1.79)

Rounding down to be sure the string does not break:

v < 11.7 m/s.

2.

If w is the angular velocity:

4.4 * 10^(-11) = 4.1 * 10^(-16) * 0.116 w^2

w = sqrt[ 4.4 * 10^(-11) / 4.1 * 10^(-16) * 0.116 ] rad/s

= sqrt[ 4.4 * 10^(-11) / 4.1 * 10^(-16) * 0.116 ] / 2pi

= 153.1 rev / s.